Solution of differential equation dy – sin x sin y dx = 0 is :
Answer & explanation
Correct answer: option 1
Given equation can be written as :
$\frac{d y}{\sin y}=\sin x d x$
$\Rightarrow \int cosec ~y~d y=\int \sin x~ d x+c$
$\Rightarrow \log \tan \frac{y}{2}=-\cos x+c_1$
$\Rightarrow \tan \frac{y}{2}=e^{-\cos x} . e^{c_1}$
$\Rightarrow e^{\cos x} . \tan \frac{y}{2}=c$
Hence (1) is the correct answer.